PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

CHAPTER 3. NON-LOCAL FEATURES IN THE PRIMORDIAL SPECTRUM
3.3 Discussion
In this chapter, our main aim has been to investigate if the CMB data support certain
non-local features—i.e. a certain repeated and characteristic pattern that extends over a
wide range of scales—in the primordial scalar power spectrum. With this goal in mind,
we have studied two models of inflation, both of which contain oscillatory terms in the
inflaton potential. The oscillations in the potential produces oscillations in the slow roll
parameters, which in turn generate oscillations in the primordial as well as the CMB
power spectra. Earlier work in this context had utilized the analytical expressions for the
primordial power spectra, obtained in the slow roll approximation, to compare such models
with the data [97, 98, 99]. Instead, we have used an accurate and efficient numerical
code to arrive at the inflationary scalar and tensor power spectra. In fact, in order to ensure
a good level of accuracy, rather than evolve a finite set of modes and interpolate, we
have evolved and computed the inflationary perturbation spectra for all the modes that
is required by CAMB to arrive at the corresponding CMB angular power spectra. While
this reflects the extent of the numerical accuracy of our computations, the efficiency of the
code can be gauged by the fact that we have able to been able to complete the required
runs within a reasonable amount of time despite such additional demands.
Prior experience, gained in a different context, had already suggested the possibility
that small and continued oscillations in the scalar power spectra can lead to a better fit
to the data [94]. This experience has been corroborated by the earlier [97, 98, 99] and our
current analysis (in this context, see, however, Ref. [100]; we shall comment further on
this point below). We find that, oscillations, such as those occur in the axion monodromy
model lead to a superior fit to the data. In fact, as far as the WMAP seven-year data is
concerned, on evaluating the CMB angular power spectrum at all the required multipoles
without any interpolation, we obtain an improvement of about13 in the least squares parameterχ
2 eff for the axion monodromy model, just as the earlier analytical efforts had [98].
The time taken to compute the uninterpolated inflationary power spectra depends not
only on the number of points required, but also on the frequency of the oscillations in the
inflaton potentials that we have considered. In the case of the axion monodromy model,
over the range of parameters that we have worked with, our code takes about 3–12 seconds
to calculate the inflationary power spectra (both scalar and tensor) for the nearly
2000k-points which are required by CAMB. While such a level efficiency seems adequate
for comparing the models of our interest with the WMAP seven-year data, we found
that evaluating the uninterpolated CMB angular power spectra for comparing with the
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